Abstract

In this paper, we consider the problem of random access in wireless local area networks (WLANs) with each station generating either elastic or inelastic traffic. Elastic traffic is usually non-real-time, while inelastic traffic is usually coming from real-time applications. We formulate a network utility maximization (NUM) problem, where the optimization variables are the persistent probabilities of the stations and the utilities are either concave or sigmoidal functions. Sigmoidal utility functions can better represent inelastic traffic sources compared to concave utility functions commonly used in the existing random access literature. However, they lead to non-convex NUM problems which are not easy to solve in general. By applying the dual decomposition method, we propose a subgradient algorithm to solve the formulated NUM problem. We also develop closed-form solutions for the dual subproblems involving sigmoidal functions that have to be solved in each iteration of the proposed algorithm. Furthermore, we obtain a sufficient condition on the link capacities which guarantees achieving the global optimal solution when our proposed algorithm is being used. If this condition is not satisfied, then we can still guarantee that the optimal value of the objective function is within some lower and upper bounds. We perform various simulations to validate our analytical models when the available link capacities meet or do not meet the sufficient optimality condition.

Highlights

  • I N a wireless network, a medium access control (MAC) protocol is used to coordinate access to the shared wireless medium for mobile stations

  • We study random access in wireless local area networks (WLANs) within the network utility maximization (NUM) framework

  • We extend the work in [1] by not restricting the utility functions to remain concave after a logarithmic change of variables, but allowing the possibilities of concave, convex, or sigmoidal utility functions

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Summary

INTRODUCTION

I N a wireless network, a medium access control (MAC) protocol is used to coordinate access to the shared wireless medium for mobile stations. We study random access in WLANs within the network utility maximization (NUM) framework. Most of the previous work in NUM-based random access (e.g., in [1]) focuses only on non-real-time applications, such as file transfer and e-mail, where the data traffic is elastic. No prior work has addressed NUM problems with sigmoidal utility functions in random access systems. We provide a sufficient condition on the wireless link capacities which guarantee our algorithm to find the exact global optimal solution of the NUM problem. If this condition is not satisfied, we can still obtain upper and lower bounds for the optimal objective value.

SYSTEM MODEL
RANDOM ACCESS WITH SIGMOIDAL AND CONCAVE UTILITIES
Dual Method
First Dual Subproblem
Centralized Algorithm for Random Access
General Optimality Conditions
OPTIMALITY AND SUB-OPTIMALITY
Optimal Solution
Sub-optimal Solution
PERFORMANCE EVALUATION
CONCLUSIONS
Full Text
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